Levy copulas are the most general concept to capture jump dependence in multivariate Levy processes. They translate the intuition and many features of the copula concept into a time series setting. A challenge faced by both, distributional and Levy copulas, is to find flexible but still applicable models for higher dim…
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48 results for “Levy copulas”
A method is developed to estimate the parameters of a Levy copula of a discretely observed bivariate compound Poisson process without knowledge of common shocks. The method is tested in a small sample simulation study. Also, the method is applied to a real data set and a goodness of fit test is developed. With the meth…
We provide an integral representation for the (implied) copulas of dependent random variables in terms of their moment generating functions. The proof uses ideas from Fourier methods for option pricing. This representation can be used for a large class of models from mathematical finance, including Lévy and affine proc…
Natural gas-fired power plants valuation and optimisation under Levy copulas and regime-switchingq-fin.MF
Study optimizes natural gas power plant valuation using Levy copulas and regime-switching models.
problem Optimizing the valuation and operation of natural gas-fired power plants under market fluctuations.
method Stochastic control problem, Levy regime-switching model, skewed Levy copulas, HJB equation, finite difference method.
result Numerical method provides optimal operating strategies and plant values based on market prices and conditions.
New model captures insurance risk dependencies efficiently.
problem Dependence modeling in sparse time series of insurance claims.
method Comb-Bernoulli model bridging Lévy copulas and zero-mixed models.
result Model enables tractable simulation, likelihood evaluation, and parameter estimation.
Novel weak MLMC scheme for Lévy-driven SDEs, applied to financial derivatives pricing.
problem Approximating solutions to Lévy-driven SDEs for financial derivatives pricing.
method Weak multilevel Monte-Carlo scheme with state space discretization of Lévy processes.
result Efficient approximation of financial derivatives pricing models.
Sibuya copulasmath.PR
The standard intensity-based approach for modeling defaults is generalized by making the deterministic term structure of the survival probability stochastic via a common jump process. The survival copula of the vector of default times is derived and it is shown to be explicit and of the functional form as dealt with in…
The first passage event for sums of dependent Lévy processes with applications to insurance riskmath.PR
For the sum process of a bivariate Lévy process with possibly dependent components, we derive a quintuple law describing the first upwards passage event of over a fixed barrier, caused by a jump, by the joint distribution of five quantities: the time relative to the time of the previous maxi…
On the modelling of multivariate counts with Cox processes and dependent shot noise intensitiesq-fin.RM
Develops a method to model multivariate count processes with Cox processes and shot noise intensities.
problem Modeling and estimating dependent count processes using granular data.
method Multivariate Cox process with shot noise intensities, connected via Lévy copulas.
result Allows for over-dispersion, auto-correlation, and realistic features in count processes.
New copulas model external shocks with different effects on system components.
problem Modeling external shocks with different impacts on system components.
method Introduced reflected maxmin (RMM) copulas to extend maxmin copulas.
result Symmetric RMM copulas relate to general RMM copulas similarly to semilinear copulas to Marshall copulas.
A new copula, the checkerboard copula, maximizes entropy and preserves dependence.
problem Choosing copula for non-continuous marginal distributions.
method Introducing the checkerboard copula, maximizing Shannon entropy.
result Checkerboard copula maximizes entropy and preserves dependence.
This paper proposes a new class of copulas which characterize the set of all twice continuously differentiable copulas. We show that our proposed new class of copulas is a new generalized copula family that include not only asymmetric copulas but also all smooth copula families available in the current literature. Spea…
We provide a set of copulas that can be interpreted as having the negative extreme dependence. This set of copulas is interesting because it coincides with countermonotonic copula for a bivariate case, and more importantly, is shown to be minimal in concordance ordering in the sense that no copula exists which is stric…
This paper develops copula-based models for forecasting multivariate realized volatility.
problem Forecasting multivariate realized volatility matrices with hidden dependence structure.
method Copula-based time series models to capture hidden dependence structure and ensure positive definiteness.
result Copula-based models achieve significant performance in volatility matrix forecasting.
We propose to use nonparametric Bernstein copulas as bivariate pair-copulas in high-dimensional vine models. The resulting smooth and nonparametric vine copulas completely obviate the error-prone need for choosing the pair-copulas from parametric copula families. By means of a simulation study and an empirical analysis…
The paper proposes a method to model financial data asynchronously using copulas.
problem Modeling intraday financial returns of multiple assets due to asynchronous data.
method Proposes a consistent estimator of the correlation coefficient for Elliptical copulas and an improved estimator for non-elliptical copulas.
result The proposed estimator reduces bias in estimating copula parameters for a general class of copulas.
Paper introduces new copulas from shock models, improving on maxmin copulas.
problem Improving on maxmin copulas for better characteristics.
method Developed RMM copulas with dependent endogenous shocks and proved convergence of iteration procedures.
result RMM copulas exhibit better characteristics than maxmin copulas, including convergence properties.
New copulas based on general partitions-of-unity and their applications to risk management (part II)q-fin.RM
New copulas fit asymmetric data in any dimension.
problem Fitting asymmetric data in arbitrary dimensions.
method Constructive approach to infinite partition-of-unity copulas.
result Solution to fitting negative binomial and Poisson copulas to data.
Impact of non-stationarity on estimating and modeling empirical copulas of daily stock returnsq-fin.ST
All too often measuring statistical dependencies between financial time series is reduced to a linear correlation coefficient. However this may not capture all facets of reality. We study empirical dependencies of daily stock returns by their pairwise copulas. Here we investigate particularly to which extent the non-st…
New copulas model multiple risk factors with tractable properties.
problem Modeling stochastic dependence in multiple risk factors.
method Introduce and study a new class of MRF copulas.
result MRF copulas are non-exchangeable and exhibit various tail dependences.
New copulas based on general partitions-of-unity (part III) - the continuous case (extended version)q-fin.RM
The paper extends copulas for continuous data, enabling tail dependence.
problem Modeling continuous data with tail dependence.
method Generates copulas using empirical data and a simple algorithm.
result Allows for positive tail dependence in copula modeling.
Paper compares MCMC-based copula methods for exchange option pricing.
problem Pricing exchange options using copulas and MCMC.
method Risk-neutral pricing, copulas, and MCMC algorithm.
result Different copula models provide similar option prices except Gumbel.
New copulas fit asymmetric data for risk management.
problem Fitting asymmetric data to copulas.
method Data-driven constructive approach to partition-of-unity copulas.
result Solution for fitting Bernstein-, negative binomial, and Poisson copulas to asymmetric data.
A new copula estimation method using classification.
problem Estimating copula density from joint and marginal distributions.
method Train a classifier to distinguish joint density from product of marginals.
result Empirically outperforms existing copula estimators.
Modelling and simulation of dependence structures in nonlife insurance with Bernstein copulasstat.ME
The study models insurance dependence using Bernstein copulas.
problem Modeling dependence structures in nonlife insurance data.
method Review and suggest fitting Bernstein copulas to empirical data.
result Monte Carlo simulation and PML estimation for aggregate losses.
This paper explores non-exchangeability in copulas from shock models and computes asymmetry bounds.
problem Understanding the non-exchangeability of copulas from shock models.
method Analyzes and computes asymmetry bounds for various copulas families.
result Sharp bounds for asymmetry measures of Marshall, maxmin, and RMM copulas.
We introduce a new functional measure of tail dependence for weakly dependent (asymptotically independent) random vectors, termed weak tail dependence function. The new measure is defined at the level of copulas and we compute it for several copula families such as the Gaussian copula, copulas of a class of Gaussian mi…
Copulas allow to learn marginal distributions separately from the multivariate dependence structure (copula) that links them together into a density function. Vine factorizations ease the learning of high-dimensional copulas by constructing a hierarchy of conditional bivariate copulas. However, to simplify inference, i…
Paper uses a new copula to model risk aggregation and capital allocation.
problem Modeling dependence between risks for risk aggregation and capital allocation.
method Uses a generalized Archimedean copula (mixed Bernstein copula) to define dependence structure and derives closed-form risk measures.
result Closed-form expressions for tail value-at-risk and allocations are derived.
Copula Analysis of Risk: A Multivariate Risk Analysis for VaR and CoVaR using Copulas and DCC-GARCHq-fin.RM
Study uses copulas and DCC-GARCH for multivariate risk analysis of VaR and CVaR.
problem Multivariate risk analysis for Value at Risk (VaR) and Conditional Value at Risk (CoVaR).
method Copulas and Dynamic Conditional Correlation (DCC)-GARCH models applied to historical financial data.
result Comparison of different copula families for goodness-of-fit and effectiveness.
A Natural Copulaq-fin.RM
A new copula minimizes distance between distributions.
problem Arbitrariness in copula choice.
method Minimizes Wasserstein distance; linear programming estimation.
result Natural copula provides parsimonious estimation.
A new class of bivariate distributions is introduced that extends the Generalized Marshall-Olkin distributions of Li and Pellerey (2011). Their dependence structure is studied through the analysis of the copula functions that they induce. These copulas, that include as special cases the Generalized Marshall-Olkin copul…
Testing the Gaussian Copula Hypothesis for Financial Assets Dependencescond-mat.stat-mech
Using one of the key property of copulas that they remain invariant under an arbitrary monotonous change of variable, we investigate the null hypothesis that the dependence between financial assets can be modeled by the Gaussian copula. We find that most pairs of currencies and pairs of major stocks are compatible with…
Adaptive Bernstein copulas improve risk management by preventing overfitting and reducing simulation effort.
problem Overfitting and high simulation effort in estimating dependence models.
method Constructive approach to Bernstein copulas with an admissible discrete skeleton.
result Comparison of different copula approaches in risk management shows improved accuracy and efficiency.
Study uses vine copulas to optimize financial portfolios during and after the financial crisis.
problem Optimizing financial portfolios during and after the financial crisis.
method Modeling dependency structures using vine copulas, testing different portfolio strategies, analyzing various copulas.
result Vine copulas reduce portfolio risk better than simple copulas, especially during the financial crisis.
The paper assesses portfolio risk using copula models.
problem Assessing portfolio risk in financial time series.
method Proposes an algorithm for risk measure computation using copula models.
result Risk curves from copula models are lower than historical values.
Gaussian copulas are widely used in the industry to correlate two random variables when there is no prior knowledge about the co-dependence between them. The perturbed Gaussian copula approach allows introducing the skew information of both random variables into the co-dependence structure. The analytical expression of…
New copula models learn to forget dependencies, improving data representation.
problem Restrictive assumptions and poor scaling in existing copula models.
method Diffusion and flow-based copulas that progressively forget dependencies.
result Provable valid copulas at all times, superior performance in complex dependencies.
Proposes copulas for heteroskedastic time series with improved volatility measures.
problem Capturing serial dependence in stationary time series with varying volatility.
method Developed parametric copulas for Markov and multivariate series, derived volatility proxy copulas, and proposed new volatility dependence measures.
result Proposed copulas outperform GARCH models in capturing volatility and producing accurate risk forecasts.
Paper proposes copula-based models for analyzing multivariate zero-inflated continuous data.
problem Challenges in analyzing multivariate zero-inflated continuous data with mixed discreteness and continuity.
method Proposes two copula-based density estimation models and rectified Gaussian copula.
result Demonstrates superior performance compared to conventional methods.
Marginals Versus Copulas: Which Account For More Model Risk In Multivariate Risk Forecasting?q-fin.RM
Copulas outperform marginal models in multivariate risk forecasting, reducing model risk by narrowing down the set of models.
problem Model risk in multivariate risk forecasting, especially during crises.
method Comprehensive empirical study comparing Copula-GARCH models with fixed marginals, copulas, or neither.
result Model risk is almost entirely due to copula choice, not marginal models.
Bayesian VI copula models capture asymmetric intraday equity dependence.
problem Modeling asymmetric and extreme tail dependence in financial data.
method Bayesian variational inference for skew-t copula models in high dimensions.
result The copula captures substantial heterogeneity in asymmetric dependence over equity pairs and time.
Characterizes symmetric Bernoulli distributions with minimal convex sums.
problem Understanding minimal dependence among Bernoulli random vectors.
method Geometric and algebraic representations of multivariate symmetric Bernoulli distributions.
result Characterizes extremal negative dependence and builds minimal dependence copulas.
The t copula is often used in risk management as it allows for modelling tail dependence between risks and it is simple to simulate and calibrate. However, the use of a standard t copula is often criticized due to its restriction of having a single parameter for the degrees of freedom (dof) that may limit its capabilit…
The study evaluates financial risk using copulas and statistical tests.
problem Validating bivariate forecasts in risk evaluation.
method Using copulas to characterize dependencies, applying statistical tests to validate forecasts, removing heteroskedasticity.
result A Student copula accurately describes financial time series dependencies.
The estimation of dependencies between multiple variables is a central problem in the analysis of financial time series. A common approach is to express these dependencies in terms of a copula function. Typically the copula function is assumed to be constant but this may be inaccurate when there are covariates that cou…
Study proposes a method to construct copulas using corrected Hermite polynomial expansion for estimating foreign exchange volatility.
problem Estimating cross foreign exchange volatility with complex correlation structures.
method Applying corrections to the finite sum of multivariate Hermite polynomial expansions to construct copulas.
result The proposed copula method accurately reproduces the volatility smile of cross currency pairs.
This paper improves tail dependence analysis by introducing a path-based approach.
problem The classical tail dependence coefficient fails to capture non-exchangeable features of tail dependence.
method The paper introduces a path-based maximal tail dependence approach to capture the most pronounced feature of dependence over all possible paths.
result The paper proves the existence and provides an explicit characterization of the path-based maximal TDC, improving analytical and computational tractability.